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Republican Donald Trump and Democrat Hillary Clinton have moved closer to winning their parties' nominations with a series of victories in the Super Tuesday elections .

Clinton and Trump each won at least seven of 11 state races as they distanced themselves from party rivals and looked ahead to the November 8 presidential election.

Ted Cruz, a Republican senator, won his home state of Texas, Alaska and Oklahoma as he sought to emerge as Trump's main rival.

Clinton's only opponent, Bernie Sanders, also won Oklahoma, as well as his home state of Vermont, Colorado and Minnesota.

Super Tuesday explained

Cruz desperately needed the Texas win in order to stay in the race, and was likely to keep campaigning as the only Republican who has been able to defeat Trump in any primary contest.

Still, Trump's wins in the South were a blow to Cruz, who once saw the region as his opportunity to stake a claim to the nomination.

Instead, he has watched Trump, a brash New York real estate mogul, display surprising strength with the region's evangelical Christians and social conservatives.

For Marco Rubio, who is also seeking to emerge as the main alternative to Trump, the night was disappointing. While Republican officeholders have rallied around him in recent days, he only managed to score a campaign win in Minnesota.

His long-shot hopes now rest with his home state, Florida, which votes on March 15, but polls show him trailing Trump there.

Signalling her confidence, Clinton set her sights on Trump as she addressed supporters during a victory rally in Miami.

"It's clear tonight that the stakes in this election have never been higher and the rhetoric we're hearing on the other side has never been lower," said Clinton, who is seeking to become America's first female president.

Trump, too, had his eye on a general election match-up with Clinton, casting her as part of a political establishment that has failed Americans.

"She's been there for so long," Trump told a news conference at his swanky Mar-a-Lago resort in Florida. "If she hasn't straightened it out by now, she's not going to straighten it out in the next four years."

Delegate score

Democrats were allocating 865 delegates on Super Tuesday, more than one-third of the 2,383 needed to become the nominee.

Clinton is now assured of winning at least 334 delegates on Tuesday and Sanders 145. Including superdelegates - party leaders who get to vote for candidates at the convention - Clinton now has at least 882 delegates. Sanders has at least 232.

For Republicans, 595 delegates were at stake, nearly half of the 1,237 needed for the nomination.

Despite Trump's string of victories on Tuesday, his delegate gains were limited by Cruz's big win in delegate-rich Texas - illustrating the importance of the March 15 primaries in Florida and Ohio in which the statewide winner gets all the delegates.

For the night, Trump won at least 234 delegates and Cruz won at least 209. Rubio was a distant third with at least 90. Overall, Trump leads with 316 delegates and Cruz has 226. Rubio has 106 delegates, John Kasich has 25 and Ben Carson has eight.

Al Jazeera's Alan Fisher, reporting from Stafford, Texas, said Trump continued to benefit from the split field in the Republican race.

"Ted Cruz believes that if you make this a two-man race he has a change of overhauling Trump, although that wouldn’t seem to be reflected in the results of Super Tuesday," he added.

"Marco Rubio has also asked the others to drop out and allow him to go head-to-head with Trump. So, while the field is so split, Donald Trump continues to rack up delegates. Of course Rubio and Cruz do as well, but in much smaller numbers."

Both Cruz and Rubio have launched furious verbal attacks on Trump in recent days, but some in the party establishment fear the anti-Trump campaign has come too late.

Republicans spent months largely letting Trump go unchallenged, wrongly assuming that his populist appeal with voters would fizzle. Instead, he has appeared to only grow stronger, winning states and drawing support for some of his most controversial proposals.

In six of the states voting Tuesday, large majorities of Republican voters said they supported a proposal to temporarily ban all non-citizen Muslims from entering the United States, an idea championed by Trump.